Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

Q: Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2<x 3 about the x-axis. 4

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Q: Find the area of the surface generated by revolving the curve y = V 121 - x2, – 1 s x < 1 about the…

A: We can find the answer as below.

Q: Find the area of the surface obtained by revolving the curve x=/y+1, for 1<y<, around the y-axis.

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Find the area of the surface obtained by rotating the curve about the x-axis y=Vx, 0sxs4

A: Please refer to the image below.

Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

Q: Find the surface area for x=3( θ – sin θ ) , y= 3(1-cos θ ). , when rotated along the x axis.

A: Given x=3θ-sin θ,  y=31-cos θ  The surface area is rotated along the x-axis. Then y=0, 31-cos…

Q: Find the area of the surface generated by revolving the curve y = 2Va, 0 <x < 3, about the x-axis.

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Q: B- Find the area of the surface generated by revolving the curve y = √√2-x² about x-axis

A: Introduction:   An object's surface area is the total area that all of its surfaces occupy. The…

Q: Find the area of the surface generated by revolving the curve 1 V1 + eb", 5x 0 < x < 2 around the…

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Q: Find the area of the surface obtained by rotating the curve y : sin x from x = 0 to x = 1.4 about…

A: Given region bounded by y= sinx  from x=0 to x=1.4

Q: Find the surface area of the solid that is obtained by rotating the graph of y = f (x) about the…

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Q: HW: Find the area of the surface generaled by revolving 1. Vy, 1 <y <8 about the x- axis. =DX

A: Find the attachment

Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

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Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: Q2) Find the area of the surface generated by revolving the curve y=√4-x² about y-axis.

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Q: Find the area of the surface generated by revolving the curve y = Væ +1, 1< x< 5about the x-axis. I…

A: surface area of the curve f(x) revolved about x-axis  A = 2π∫abfx1+f'x2dx

Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x-axis. A…

A: Area of surface generated by rotating a curve y=f(x) from x=a to x=b about x-axis  A=∫ab2πydsWhere…

Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: The area of the surface obtained by rotating the curve y = V25–x2, -4 < x s 4 about the x-axis is

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Q: Find the area of the surface generated by revolving the curve x =- =t/2,y = 2Vt; 0<t< v3 about the…

A: We solve the problem by using formula of area of surface generated by revolving curves about y axis.…

Q: Find the surface area of the object obtained by rotating y = +÷, 1 1<x<2 about the x-axis.

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: Find the surface area of the solid that is obtained by rotating the graph of y = f(x) about the…

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Q: Find the surface area of the solid generated by rotating the curve y = x² about the y-axis over the…

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Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: HW: Find the area of the surface generaled by revolving 3DVy, 1 <y<8 about the X- axis. 1. 3.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: Find the area of the surface generated by revolving the following curve alongthe x-axis: x = 2t3,y =…

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Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: Find the surface area of the solid gained by revolving the curve 0 < x < 14, about the x – axis. 14'

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Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the area of the surface generated by revolving the curve x = 6t , y = 4t2 for t = 0 to t = 1…

A: Differentiate the equations x=6t and y=4t2 with respect to t, to find dxdt and dydt.…

Q: Find the area of the surface obtained by rotating the curve y=1+3x² from x = 0 to x = 9 about the…

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Q: Find the area of the surface generated by revolving the curve y =,0sx<2, about the x-axis.

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Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: Find the area of the surface obtained by rotating the curve y=1/33/2, 0 ≤ y≤12  about the y - axis.

A: To find the area of the surface obtained by rotating the curve

Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: Find the area of the surface obtained by rotating the curve y=1/3 x3/2, 0≤y≤12  about the y- axis.

A: Let a rectangular strip parallel to x-axis of thickness dy be made whose tip touches the curve…

Q: Find the area of the surface resulting from rotating the curve: x=5t−1, y=2t^3, -2≤t≤1, around the…

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Q: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: Find the area of the surface obtained by rotating the following curve about the x-axis. y=2x3 , 0…

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Q: The area of the surface obtained by rotating the curve x = y2 - In(Vy), 1sys2 about the x-axis is

A: The given curve is: x=14y2-lny  ;      1≤y≤2 Therefore: dxdy=y2-12y

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.